The minister would circulate a draft resolution which proposed four steps:
• An unequivocal call for an end to the violence, and for leaders to use their authority to bring the violence to an end.
• Reaffirm the "unambiguous commitment" of the UNSC to a two-state solution.
• Make it clear that any solution must take place through direct talks between parties.
• If the parties are not ready, a course should be charted for direct talks.
Mr McCully said the two parties should prepare for talks "within a realistic but early timeframe".
He added: "While no words from this Council will themselves bring about a solution to the Palestinian question, it is our duty today to find ways to stem the violence, and then to find a framework that creates space for the diplomacy and political engagement that are so seriously overdue."
New Zealand is 10 months into a two-year term as a non-permanent member of the UNSC.